Solving Optimal Electric Vehicle Charger Deployment Problem
Abstract
:1. Introduction
- Building a comprehensive mathematical framework accommodating the particular complexity,
- Demonstrating our numerical computational framework for solving the facility location problem (FLP) representing the optimal location;
- Laying out an extensive comparative study among the optimization solving techniques as an effort to find the most efficient solver;
- Applying the findings to two real-world case studies representing an average and high density of EVs.
2. Related Work
2.1. Problem Formulation Approaches
2.1.1. Facility Location Problem (FLP)
2.1.2. Distance Optimization
2.1.3. Weight Assignment Techniques
2.1.4. Machine Learning Techniques
2.2. Solving Techniques
3. Problem Formulation
3.1. Spatial Setup
3.2. Formulation to Capacitated FLP
- i and j are indexes for an EV charging facility and a demanding area (or, equivalently, a customer), respectively.
- gives the variable cost to obtain the electricity supplied to serve customer j.
- gauges the demand from customer j.
- quantifies the fraction of the demand made by customer j and fulfilled by facility i.
- indicates whether facility i opens or not.
- denotes the sunken cost (also known as “fixed” cost) of opening a charging facility i.
- defines the equity achieved at customer j via service from facility i.
- and indicate the capacity of facility i and the required minimum capacity of any facility, respectively, both in the unit of kWh.
3.3. Unique Challenges
- C1: Large search spaces for domain and other variables;
- C2: Inexistence of polynomial-time numerical solving. techniques
4. Solving Techniques Development
4.1. Unique Challenges and Proposed Approaches
4.2. Comparison among Solving Techniques
4.3. Alternative Techniques
5. Case Study 1: Region with Average EV Density
5.1. Case-Specific Refinement of Solving Method
5.2. Results and Discussion
Algorithm 1 SA implemented in this work |
|
6. Case Study 2: Region with High EV Density
6.1. Case-Specific Refinement of Solving Method
6.1.1. Data Collection and Preprocessing
6.1.2. Data Integration
6.1.3. Training Methods
- Data Preparation: The collected and merged dataset undergoes preprocessing to ensure its suitability for training, including handling missing values, data normalization, and feature engineering.
- Training Process: Each selected model is trained using the prepared dataset, which is divided into training and validation sets. Performance evaluation metrics such as accuracy, precision, recall, and F1 score are utilized to assess the model’s performance during training.
- Model Evaluation: After training, the models are evaluated using the validation set to assess their predictive capabilities. The evaluation metrics are used to compare the models’ performance and identify the model with the highest accuracy or other desired performance metrics.
- Model Selection: Based on the evaluation results, the model demonstrating the best performance is selected as the final machine learning model for the site selection task.
6.2. Results and Discussions
- Installation criteria differ between DC fast chargers and level-2 chargers. Significant differences in consistency are observed when training separately based on each charging station type or when training with both types together. Consequently, it can be concluded that chargers have been installed at locations that meet their respective criteria for both DC fast chargers and level-2 chargers.
- Non-uniform distribution of reference data does not significantly affect training results. There is no significant difference in consistency between training based on non-uniformly distributed chargers and training based on grid points uniformly distributed at regular intervals. Thus, it can be concluded that the non-uniform distribution of data does not impact the training results.
- Buffer size influences data consistency. Decreasing the buffer size results in increased consistency. The reason for the decrease in consistency at buffer sizes below 125 m is that the polygon data used for learning is 250 m × 250 m grid data, resulting in buffers that do not contain data from the 125 m radius buffer size. This problem can be solved by using smaller grid data than 250 m × 250 m grid data during data preprocessing. In conclusion, this result shows that larger buffer sizes increase data redundancy and affect consistency.
7. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Literature | Contribution |
---|---|
FLP | Formulation into MINLP for various real-world problems |
Distance Optimization | Stochastic analyses for location selection |
Weight Assignment Techniques | Demand prediction by assigning weights to data |
Machine Learning Techniques | More efficient weight assignment via priority prediction |
Solving Techniques | Exact or heuristic approaches to solve NP-hard problems |
This Paper | Comprehensive feasibility study encompassing the aforementioned numerical techniques |
Solver | ⋯ | Objective Value | Number of Iterations | |||
---|---|---|---|---|---|---|
Integer Linear Programming | ⋯ | 0 | 0 | |||
Pattern Search | 0 | 0 | ⋯ | 0 | 0 | 204 |
Genetic Algorithm | −0.062657 | 0.042974 | ⋯ | −0.041941 | 1.4801 | 3907 |
Particle Swarm | ⋯ | 4320 | ||||
Simulated Annealing | −1.99 | ⋯ | 0.00018799 | 3.9798 | 3008 | |
Surrogate Optimization | 0.99678 | 1.9937 | ⋯ | 1.9832 | 8.9671 | 200 |
Model Name | Decision Tree | Support Vector Machine | Random Forest |
---|---|---|---|
Consistency | 0.6583 | 0.4295 | 0.7580 |
Precision | 0.6712 | 0.1845 | 0.7580 |
Recall | 0.6583 | 0.4295 | 0.7580 |
F1-Score | 0.6593 | 0.2581 | 0.7509 |
Setting Condition | Buffer Size | Consistency | |
---|---|---|---|
Baseline | Public DC fast chargers and random point | 1.13 km | 0.7580 |
a. Charging Station Type | Public level-2 chargers and random point | 1.13 km | 0.7678 |
Public DC fast chargers and public level-2 chargers and random point | 1.13 km | 0.6284 | |
b. Uniform Distribution of Reference Data | Center point of grid data | 1.13 km | 0.7649 |
c. Buffer size | Public DC fast chargers and random point | 700 m | 0.8176 |
600 m | 0.8355 | ||
500 m | 0.8611 | ||
400 m | 0.8743 | ||
300 m | 0.9003 | ||
200 m | 0.9182 | ||
150 m | 0.9348 | ||
125 m | 0.9395 | ||
100 m | 0.9293 | ||
50 m | 0.8969 |
Data | Variable Importance [%] |
---|---|
POI | 16.9264 |
Surface | 12.9745 |
Building0 | 11.3435 |
Work_Population | 9.4463 |
Building3 | 8.1137 |
Traffic | 7.3983 |
Building1 | 6.768 |
Flow_Population | 5.7931 |
Car | 5.4492 |
EV_Car | 5.3769 |
Parking | 4.2025 |
Tour | 3.563 |
Building2 | 2.6447 |
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Kim, S.; Jeong, Y.; Nam, J.-W. Solving Optimal Electric Vehicle Charger Deployment Problem. Appl. Sci. 2024, 14, 5092. https://doi.org/10.3390/app14125092
Kim S, Jeong Y, Nam J-W. Solving Optimal Electric Vehicle Charger Deployment Problem. Applied Sciences. 2024; 14(12):5092. https://doi.org/10.3390/app14125092
Chicago/Turabian StyleKim, Seungmo, Yeonho Jeong, and Jae-Won Nam. 2024. "Solving Optimal Electric Vehicle Charger Deployment Problem" Applied Sciences 14, no. 12: 5092. https://doi.org/10.3390/app14125092
APA StyleKim, S., Jeong, Y., & Nam, J.-W. (2024). Solving Optimal Electric Vehicle Charger Deployment Problem. Applied Sciences, 14(12), 5092. https://doi.org/10.3390/app14125092